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Two places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet each other in 8 hours. If they move in opposite directions towards each other, they meet in 1 hour 20 minutes. Determine the speed of the faster car.
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- 20 kmph
- 25 kmph
- 35 kmph
- 30 kmph
Correct Option: C
Case : I
When the cars are moving in the same direction.
Let A and B be two places and C be the place of meeting.
Let the speed of car starting from A be x kmph, and that of car starting from B be y kmph.
Relative speed = (x – y) kmph
According to the question.
(x – y) × 8 = 80
⇒ x – y = 10 ...(i)
Case : II
When the cars are moving in the opposite directions and they meet at point C.
Relative speed = (x + y) kmph
Time taken = 1 hour 20 minutes
| = 1 + | = | hours | ||
| 3 | 3 |
| ∴ (x + y) × | = 80 | |
| 3 |
| ⇒ x + y = | |
| 4 |
⇒ x + y = 60 ...(ii)
Adding equations (i) and (ii),
2x = 70
⇒ x = 35
From equation (ii),
x + y = 60
⇒ 35 + y = 60
⇒ y = 60 – 35 = 25
∴ Speed of the faster car = 35 kmph
